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1.
The Hom complex of homomorphisms between two graphs was originally introduced to provide topological lower bounds on the chromatic
number. In this paper we introduce new methods for understanding the topology of Hom complexes, mostly in the context of Γ-actions
on graphs and posets (for some group Γ). We view the Hom(T, ⊙) and Hom(⊙, G) complexes as functors from graphs to posets, and introduce a functor (⊙)1 from posets to graphs obtained by taking atoms as vertices. Our main structural results establish useful interpretations
of the equivariant homotopy type of Hom complexes in terms of spaces of equivariant poset maps and Γ-twisted products of spaces.
When P:= F(X) is the face poset of a simplicial complex X, this provides a useful way to control the topology of Hom complexes. These constructions generalize those of the second
author from [17] as well as the calculation of the homotopy groups of Hom complexes from [8]. 相似文献
2.
In this paper, we continue the investigation of an estimator proposed in [Yu. Davydov, V. Paulauskas, and A. Račkauskas, More
on p-stable convex sets in Banach spaces, J. Theor. Probab., 13:39–64, 2000] and [V. Paulauskas, A new estimator for tail index, Acta Appl. Math., 79:55–67, 2003] and considered in [V. Paulauskas and M. Vaičiulis, Once more on comparison of tail index estimators, preprint, 2010]. We propose a class of modifications of the so-called DPR estimator and demonstrate that these modifications can have better
asymptotic properties than the original DPR estimator. 相似文献
3.
M. C. Crabb 《Journal of Fixed Point Theory and Applications》2007,2(2):171-193
We describe an equivariant version (for actions of a finite group G) of Dold’s index theory, [10], for iterated maps. Equivariant Dold indices are defined, in general, for a G-map U → X defined on an open G-subset of a G-ANR X (and satisfying a suitable compactness condition). A local index for isolated fixed-points is introduced, and the theorem
of Shub and Sullivan on the vanishing of all but finitely many Dold indices for a continuously differentiable map is extended
to the equivariant case. Homotopy Dold indices, arising from the equivariant Reidemeister trace, are also considered.
相似文献
4.
We develop an integral version of Deligne cohomology for smooth proper real varieties. For this purpose the role played by singular cohomology in the complex case has to be replaced by the ordinary bigraded
Gal(\mathbbC/\mathbbR){Gal(\mathbb{C}/{\mathbb{R}})}-equivariant cohomology of Lewis et al. (Bull Am Math Soc (N.S.) 4(2):208–212, 1981), the equivariant counterpart of singular cohomology. The theory is aimed at giving more precise information about the 2-primary
components of regulators. We establish basic properties and give a geometric interpretation for the groups in dimension 2
in weights 1 and 2. 相似文献
5.
This is the first of a series of papers on partition functions and the index theory of transversally elliptic operators. In
this paper we only discuss algebraic and combinatorial issues related to partition functions. The applications to index theory
are in [4], while in [5] and [6] we shall investigate the cohomological formulas generated by this theory. 相似文献
6.
Roland Lötscher 《Transformation Groups》2010,15(3):611-623
We investigate the essential dimension of finite groups using the multihomogenization technique introduced in [KLS09], for which we provide new applications in a more general setting. We generalize the central extension theorem of Buhler
and Reichstein [BR97, Theorem 5.3] and use multihomogenization as a substitute to the stackinvolved part of the theorem of Karpenko and Merkurjev
[KM08] about the essential dimension of p-groups. 相似文献
7.
Christopher T. Woodward 《Geometric And Functional Analysis》2011,21(3):680-749
We investigate the small area limit of the gauged Lagrangian Floer cohomology of Frauenfelder [Fr1]. The resulting cohomology theory, which we call quasimap Floer cohomology, is an obstruction to displaceability of Lagrangians in the symplectic quotient. We use the theory to reproduce the results
of Fukaya–Oh–Ohta–Ono [FuOOO3,1] and Cho–Oh [CO] on non-displaceability of moment fibers of not-necessarily-Fano toric varieties and extend their results to toric orbifolds,
without using virtual fundamental chains. Finally, we describe a conjectural relationship with Floer cohomology in the quotient. 相似文献
8.
Hiroshi Iritani 《Mathematische Zeitschrift》2006,252(3):577-622
The objective of this paper is to clarify the relationships between the quantum D-module and equivariant Floer theory. Equivariant Floer theory was introduced by Givental in his paper ``Homological Geometry'.
He conjectured that the quantum D-module of a symplectic manifold is isomorphic to the equivariant Floer cohomology for the universal cover of the free loop
space. First, motivated by the work of Guest, we formulate the notion of ``abstract quantum D-module' which generalizes the D-module defined by the small quantum cohomology algebra. Second, we define the equivariant Floer cohomology of toric complete
intersections rigorously as a D-module, using Givental's model. This is shown to satisfy the axioms of abstract quantum D-module. By Givental's mirror theorem [Giv3], it follows that equivariant Floer cohomology defined here is isomorphic to the
quantum cohomology D-module. 相似文献
9.
We consider arithmetic varieties endowed with an action of the group scheme of n-th roots of unity and we define equivariant arithmetic K
0-theory for these varieties. We use the equivariant analytic torsion to define direct image maps in this context and we prove
a Riemann-Roch theorem for the natural transformation of equivariant arithmetic K
0-theory induced by the restriction to the fixed point scheme; this theorem can be viewed as an analog, in the context of Arakelov
geometry, of the regular case of the theorem proved by P. Baum, W. Fulton and G. Quart in [BaFQ]. We show that it implies
an equivariant refinement of the arithmetic Riemann-Roch theorem, in a form conjectured by J.-M. Bismut (cf. [B2, Par. (l),
p. 353] and also Ch. Soulé’s question in [SABK, 1.5, p. 162]).
Oblatum 22-I-1999 & 20-II-2001?Published online: 4 May 2001 相似文献
10.
11.
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13.
In (Gluskin, Litvak in Geom. Dedicate 90:45–48, [2002]) it was shown that a polytope with few vertices is far from being symmetric in the Banach–Mazur distance. More precisely,
it was shown that Banach–Mazur distance between such a polytope and any symmetric convex body is large. In this note we introduce
a new, averaging-type parameter to measure the asymmetry of polytopes. It turns out that, surprisingly, this new parameter
is still very large, in fact it satisfies the same lower bound as the Banach–Mazur distance. In a sense it shows the following
phenomenon: if a convex polytope with small number of vertices is as close to a symmetric body as it can be, then most of its vertices
are as bad as the worst one. We apply our results to provide a lower estimate on the vertex index of a symmetric convex body, which was recently introduced
in (Bezdek, Litvak in Adv. Math. 215:626–641, [2007]). Furthermore, we give the affirmative answer to a conjecture by Bezdek (Period. Math. Hung. 53:59–69, [2006]) on the quantitative illumination problem. 相似文献
14.
Olav Arnfinn Laudal 《Acta Appl Math》2008,101(1-3):191-204
In the papers (Laudal in Contemporary Mathematics, vol. 391, [2005]; Geometry of time-spaces, Report No. 03, [2006/2007]), we introduced the notion of (non-commutative) phase algebras (spaces) Ph
n
(A), n=0,1,…,∞ associated to any associative algebra A (space), defined over a field k. The purpose of this paper is to study this construction in some more detail. This seems to give us a possible framework
for the study of non-commutative partial differential equations. We refer to the paper (Laudal in Phase spaces and deformation
theory, Report No. 09, [2006/2007]), for the applications to non-commutative deformation theory, Massey products and for the construction of the versal family
of families of modules. See also (Laudal in Homology, Homotopy, Appl. 4:357–396, [2002]; Proceedings of NATO Advanced Research Workshop, Computational Commutative and Non-Commutative Algebraic Geometry, [2004]).
相似文献
15.
Brant C. Jones 《Journal of Algebraic Combinatorics》2009,29(2):229-260
We show that the leading coefficient of the Kazhdan–Lusztig polynomial P
x,w
(q) known as μ(x,w) is always either 0 or 1 when w is a Deodhar element of a finite Weyl group. The Deodhar elements have previously been characterized using pattern avoidance
in Billey and Warrington (J. Algebraic Combin. 13(2):111–136, [2001]) and Billey and Jones (Ann. Comb. [2008], to appear). In type A, these elements are precisely the 321-hexagon avoiding permutations. Using Deodhar’s algorithm (Deodhar in Geom. Dedicata
63(1):95–119, [1990]), we provide some combinatorial criteria to determine when μ(x,w)=1 for such permutations w.
The author received support from NSF grants DMS-9983797 and DMS-0636297. 相似文献
16.
Brett Milburn 《Differential Geometry and its Applications》2011,29(5):615-641
The aim of this paper is to study generalized complex geometry (Hitchin, 2002) [6] and Dirac geometry (Courant, 1990) [3], (Courant and Weinstein, 1988) [4] on homogeneous spaces. We offer a characterization of equivariant Dirac structures on homogeneous spaces, which is then used to construct new examples of generalized complex structures. We consider Riemannian symmetric spaces, quotients of compact groups by closed connected subgroups of maximal rank, and nilpotent orbits in sln(R). For each of these cases, we completely classify equivariant Dirac structures. Additionally, we consider equivariant Dirac structures on semisimple orbits in a semisimple Lie algebra. Here equivariant Dirac structures can be described in terms of root systems or by certain data involving parabolic subalgebras. 相似文献
17.
M. Abellanas G. Hernández A. L. Bajuelos I. Matos B. Palop 《Journal of Mathematical Sciences》2009,161(6):909-918
A point q is embraced by a set of points S if q is interior to the convex hull of S [8]. In some illumination applications where points of S are lights and q is a point to be illuminated, the embracing concept is related to a good illumination [4, 6], also known as the ∆-guarding [12] and the well-covering [10]. In this paper, we are not only interested in convex dependency (which is actually the embracing notion) but also in proximity.
Suppose that the sites of S are lights or antennas with limited range; due to their limited power, they cover a disk of a given radius r centered at the sites of S. Only the points lying in such disks are illuminated. If we want to embrace the point q with the minimum range r, we need to know which is the closest light s
q
to q such that q lies in the convex hull formed by s
q
and the lights of S closer to q than s
q
. This subset of S related to point q is called the closest embracing set for q in relation to S and its cardinality is the closest embracing number of q. By assigning every point q in the convex hull of S to its closest embracing site s
q
, we obtain a partition of the convex hull that we call the embracing Voronoi diagram of S. This paper proves some properties of the embracing Voronoi diagrams and describes algorithms to compute such diagrams, as
well as the levels in which the convex hull is decomposed regarding the closest embracing number. 相似文献
18.
In this article we first study an equivariant cyclic cohomology for weak H-module agebras over a weak Hopf algebra H with a bijective antipode. Then we define an equivariant K-theory for weak quantum Yetter–Drinfeld algebras over H and establish a generalized Connes' pairing between the equivariant cyclic cohomology and the equivariant K-theory. As an application we consider our theory for groupoids. 相似文献
19.
Tim Austin 《Journal d'Analyse Mathématique》2010,111(1):131-150
We offer a new proof of the Furstenberg-Katznelson multiple recurrence theorem for several commuting probability-preserving
transformations T
1, T
2, …, T
d
: ℤ ↷ (X, ∑, μ) ([6]), and so, via the Furstenberg correspondence principle introduced in [5], a new proof of the multi-dimensional Szemerédi Theorem. We bypass the careful manipulation of certain towers of factors
of a probability-preserving system that underlies the Furstenberg-Katznelson analysis, instead modifying an approach recently
developed in [1] to pass to a large extension of our original system in which this analysis greatly simplifies. The proof is then completed
using an adaptation of arguments developed by Tao in [13] for his study of an infinitary analog of the hypergraph removal lemma. In a sense, this addresses the difficulty, highlighted
by Tao, of establishing a direct connection between his infinitary, probabilistic approach to the hypergraph removal lemma
and the infinitary, ergodic-theoretic approach to Szemerédi’s Theorem set in motion by Furstenberg [5]. 相似文献
20.
In this paper we prove that there exists no function F(m, p) (where the first argument is an integer and the second a prime) such that, if G is a finite permutation p-group with m orbits, each of size at least p
F(m,p), then G contains a fixed-point-free element. In particular, this gives an answer to a conjecture of Peter Cameron; see [4], [6]. 相似文献